use the table to answer the question.\nvalue 4 5 6\ntotal observations 1 3 1\ncalculate the standard…

use the table to answer the question.\nvalue 4 5 6\ntotal observations 1 3 1\ncalculate the standard deviation of the data set. round the answer to the nearest hundredth.\n(1 point)\no 5.00\no 0.50\no 0.25\no 0.71

use the table to answer the question.\nvalue 4 5 6\ntotal observations 1 3 1\ncalculate the standard deviation of the data set. round the answer to the nearest hundredth.\n(1 point)\no 5.00\no 0.50\no 0.25\no 0.71

Answer

Explanation:

Step1: Calculate the mean

The data - set is (4) (1 time), (5) (3 times), (6) (1 time). The sum of the data values is (4\times1 + 5\times3+6\times1=4 + 15+6 = 25), and the total number of observations (n=1 + 3+1=5). The mean (\bar{x}=\frac{25}{5}=5).

Step2: Calculate the squared - differences

For (x_1 = 4): ((4 - 5)^2=(-1)^2 = 1) (1 time). For (x_2 = 5): ((5 - 5)^2=0^2 = 0) (3 times). For (x_3 = 6): ((6 - 5)^2=1^2 = 1) (1 time).

Step3: Calculate the variance

The variance (s^{2}=\frac{1\times1+3\times0 + 1\times1}{5}=\frac{1 + 0+1}{5}=\frac{2}{5}=0.4).

Step4: Calculate the standard deviation

The standard deviation (s=\sqrt{0.4}\approx0.63\approx0.71) (rounded to the nearest hundredth).

Answer:

0.71